In the Regge-Teitelboim model, gravity is described by embedding the space-time manifold in a (usually flat) fixed higher-dimensional background, where the embedding coordinates, rather than the metric tensor, are the dynamical degrees of freedom. Stern and Xu extended the Regge-Teitelboim framework to encompass scenarios where the background embedding space is not flat, noting that when the background is a five-dimensional de Sitter space, the Robertson-Walker manifold undergoes a transition from a decelerating phase to an accelerating one. Previously, we constrained this model using only low-redshift observations. Here, we further explore the observational constraints on this scenario and report significantly more stringent constraints by including high-redshift data, specifically from the cosmic microwave background. Our results are consistent with the $\mathrm{\Lambda }$ cold dark matter model, with the putative model-specific energy component responsible for the recent acceleration being constrained to ${\mathrm{\Omega }}_{\mathrm{RT}}<0.006$ and the de Sitter curvature radius in units of the Hubble constant being constrained to $L{H}_0>1.45$, both at the 95% confidence level.

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• Alternative gravity theories
• Cosmological parameters
• Cosmology
• Dark energy